Understanding the Honey Barrel Problem

Let’s break down the problem step by step! We have two barrels filled with honey. Both barrels start with the same amount of honey. Let's call the amount of honey each barrel had at first X gallons.

Step 1: Drawing Out Honey

From the first barrel, we take out 37 gallons of honey. So, the first barrel now has:

X - 37 gallons.

From the second barrel, we take out 7 gallons of honey. Now, the second barrel has:

X - 7 gallons.

Step 2: Understanding the Remaining Honey

The problem tells us that what is left in one barrel is seven times what is left in the other barrel. Let’s write this as an equation:

X - 37 = 7(X - 7)

Step 3: Solving the Equation

Now we will solve the equation:

1. Start with the equation: X - 37 = 7(X - 7)

2. Expand the right side: X - 37 = 7X - 49

3. Next, we want to get all X terms on one side. So, we subtract X from both sides:

-37 = 6X - 49

4. Now add 49 to both sides:

12 = 6X

5. Finally, divide both sides by 6 to find X:

X = 2

Step 4: Finding the Amount of Honey

This means that each barrel originally contained 2 gallons of honey.

Conclusion

So, at the beginning, both barrels started with 2 gallons of honey!